Is complement of LL(k) grammar context free?
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In general, the complement of a contextfree language is not contextfree. However, LL(k) languages are a strict subset of the deterministic CFLs. The complement of a DCFL is also a DCFL, because it can be recognized by the same deterministic pushdown automaton, just with the "accept" and "reject" states swapped. So the answer to your question appears to be "yes, in fact it is deterministic contextfree." 

